Question

Решите, пожалуйста:
1) (1 - cos^2L) * (1 + tg^2L)
2) sin^4L + sin^2L*cos^2L + cos^2L
3) (sin^3L + cos^3L) / (sinL + cosL)
4) (sin^2L + 2cos^2L - 1) / ctg^2L

Answer 1

(1 - cos^2L) * (1 + tg^2L) =sin^2L * (1 + sin^2L/cos^2L)=sin^2L * ((cos^2L + sin^2L)/cos^2L)=sin^2L * (1/cos^2L)=sin^2L/cos^2L)=tg^2L


sin^4L + sin^2L*cos^2L + cos^2L=sin^2L*sin^2L + sin^2L*cos^2L + cos^2L=sin^2L*(sin^2L + cos^2L) + cos^2L=sin^2L*(1) + cos^2L= 1


(sin^3L + cos^3L) / (sinL + cosL)= (sinL + cosL)(sin^2L- sinL*cosL+ cos^2L) / (sinL + cosL)=(sin^2L- sinL*cosL+ cos^2L) =1 - sinL*cosL


(sin^2L + 2cos^2L - 1) / ctg^2L=(sin^2L + cos^2L + cos^2L - 1) / ctg^2L=(1 + cos^2L - 1) / ctg^2L=cos^2L / ctg^2L=cos^2L / cos^2L/sin^2L=cos^2L * sin^2L/ cos^2L= sin^2L